Active differential resistors with reduced noise

ABSTRACT

A method and system of providing an active differential resistor. The active differential resistor includes a diode having a first node and a second node. There is a capacitor coupled in series between the first node of the diode and an input of the active differential resistor. There is a current source coupled across the first node and the second node of the diode and configured to forward bias the diode such that a Johnson-Nyquist noise of the active differential resistor is replaced by a shot noise.

CROSS-REFERENCE TO RELATED APPLICATION

The present application claims the benefit of priority under 35 U.S.C.§119 from U.S. Provisional Patent Application Ser. No. 62/257,058entitled “Active Differential Resistor with Reduced Noise” filed on Nov.18, 2015, which is hereby incorporated by reference in its entirety forall purposes.

BACKGROUND

Technical Field

This disclosure generally relates to resistors, and more particularly,to active differential resistors that have reduced noise.

Description of Related Art

Resistors are fundamental and commonly used components in electroniccircuits. Passive resistors generate what is known as Johnson-Nyquist orthermal noise. Such noise is generated by the thermal agitation of thecharge carriers (e.g., electrons) inside a passive resistor regardlessof whether a voltage is applied. Johnson-Nyquist noise is white in thatits power spectral density is uniform throughout the frequency spectrum.It is governed by the relationship of Equation 1:

V _(John) /√{square root over (Hz)}=√{square root over (4kTR)}  [EQ. 1]

Where:

-   -   k is the Boltzmann's constant (joules per kelvin);    -   T is the resistor's absolute temperature (kelvin); and    -   R is the resistance of the resistor (Ω).

The Johnson-Nyquist noise is generally considered to be a noise limit ofa resistor and therefore an unavoidable source of error and/or undesiredrandom disturbance for many applications that use a resistor. Reducingor overcoming the Johnson-Nyquist noise could dramatically change theapplication of resistors in various circuits.

BRIEF DESCRIPTION OF DRAWINGS

The drawings are of illustrative embodiments. They do not illustrate allembodiments. Other embodiments may be used in addition or instead.Details that may be apparent or unnecessary may be omitted to save spaceor for more effective illustration. Some embodiments may be practicedwith additional components or steps and/or without all of the componentsor steps that are illustrated. When the same numeral appears indifferent drawings, it refers to the same or like components or steps.

FIGS. 1A and 1B illustrate example active differential resistors thatmay be used to replace passive resistors.

FIGS. 2A and 2B illustrate other embodiments of active differentialresistors that use a field effect transistor (FET) as an activecomponent.

FIGS. 3A and 3B illustrate other embodiments of active differentialresistors that use a FET and a transformer to implement an activedifferential resistor that may be used to replace a passive resistor.

FIG. 4 illustrates an example of an active differential resistorconnected across an end of a transmission line and configured to operateas a low noise termination of that line.

FIG. 5 illustrates an example of an active differential resistorconnected across an input of an electronic amplifier and configured tooperate as part of an automated test equipment that determines a levelof noise generated by the electronic amplifier.

FIG. 6 illustrates an example of an active differential resistorconnected across an output of a physical sensor.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

In the following detailed description, numerous specific details are setforth by way of examples in order to provide a thorough understanding ofthe relevant teachings. However, it should be apparent that the presentteachings may be practiced without such details. In other instances,well-known methods, procedures, components, and/or circuitry have beendescribed at a relatively high-level, without detail, in order to avoidunnecessarily obscuring aspects of the present teachings. Someembodiments may be practiced with additional components or steps and/orwithout all of the components or steps that are described.

The methods and circuits disclosed herein generally relate to methodsand circuits of providing low noise resistance elements. Moreparticularly, the present disclosure describes active differentialresistors that have less noise than passive resistors. In variousembodiments, the active device noise is set by shot noise that can belower than the Johnson-Nyquist noise of a conventional passive resistor.

In various embodiments, the active differential resistor may include adiode having a first node and a second node. There is a capacitorcoupled in series between the first node of the diode and an input ofthe active differential resistor. There is a current source coupledacross the first node and the second node of the diode and configured toforward bias the diode such that a Johnson-Nyquist noise of the activedifferential resistor is replaced by a shot noise.

In one embodiment, the active differential resistor includes a fieldeffect transistor (FET) having a drain coupled to the input node and asource coupled to the output node. A first voltage source circuit iscoupled between the drain and the source of the FET. A second voltagesource circuit is coupled between a gate and the source of the FET. Thefirst and the second voltage source circuits are configured to bias theFET into the saturation region such that the Johnson-Nyquist noise ofthe active differential resistor is replaced by shot noise.

In one embodiment, an active differential resistor includes a FET havinga drain coupled to the input node and a source coupled to the outputnode. There is a transformer having a primary winding and a secondarywinding, wherein the first end of the primary winding is connected to agate of the FET and the first end of the secondary winding is connectedto the drain of the FET. Two voltage sources are configured to bias theFET into or near the saturation region such that the Johnson-Nyquistnoise of the active differential resistor is replaced by shot noise. Theconcepts discussed herein ultimately provide a noise-floor that is lowerthan that of a passive resistor.

FIGS. 1A and 1B illustrate example active differential resistors 100Aand 100B that may be used to replace passive resistors. Activedifferential resistors 100A and 100B each include a diode D1 (108), acurrent source 120, and a blocking capacitor 106. In variousembodiments, the blocking capacitor C1 may be coupled between a firstnode 102 and the anode of the diode D1 (108), as illustrated in FIG. 1A,or between the cathode of the diode D1 (108) and the second node 104 ofthe active differential resistor 100B, as illustrated in FIG. 1B.

The blocking capacitor 106A/B provides more flexibility (e.g., broaderapplication) to the active differential resistor 100A/B in that itdecouples the blocking capacitor C1 (106) from any circuit that iscoupled between its differential inputs 102 and 104. Put differently, byvirtue of the decoupling capacitor C1 (106) the active differentialresistor 100A/B can be used in a voltage environment that is independentof the voltage environment of a circuit coupled to the activedifferential resistor environments.

In one embodiment, the capacitance value of the blocking capacitor C1(106A/B) is based on the lowest desired frequency of operation of thedifferential resistor 100A/B.

For purposes of simplicity, the examples of FIGS. 1A and 1B illustrate adiode 108 to be coupled between the first node 102 and the second node104 of the active differential resistors 100A and 100B, respectively. Inthis regard, it is noted that other devices having PN junctions can beused instead, including (without limitation) a junction gatefield-effect transistor (JFET) where the drain and source are coupledtogether. For example, the gate can function as the cathode and thedrain/source can function as the anode for a p-channel JFET, and theopposite for an n-channel JFET. In another embodiment, a monolithicinsulated gate field effect transistor (MOSFET) can be used, where thegate, drain and source are all coupled together and the substrate diodeis used in place of diode 108. In yet another embodiment, a verticalfield effect transistor (VDMOS) can be used, where the gate and sourceare coupled together and the body diode is used in place of diode 108.

The active differential resistor 100A/B includes a current source 120connected across (e.g., in parallel with) the diode 108 such that thecurrent source 120 forward biases the diode 108. By virtue of thecurrent source 120 coupled in parallel to the diode 108, which forwardbiases the diode 108, the diode 108 is configured to operate as adifferential resistance element.

Any suitable current source may be used to bias the diode 108. Forexample, a current source may include a voltage source 112 coupled inseries with a resistor R1 110. It is believed that those skilled in theart are familiar with other suitable current source structures, and theyare therefore not discussed here for brevity.

It may be helpful now to provide an example of values of components thatmay be used to implement active differential resistor to better explainthe operation of the active differential resistor 100A/B. The valuesdiscussed below are provided by way of example only and not limitationfor a 1KΩ resistor. For example, the current source 120 may source about25.7 uA through the diode D1 (108). In this regard, the impedancebetween nodes 102 and 104 of the active differential resistor 100A maybe nominally 1KΩ at frequencies above 1 KHz. As mentioned previously,the lower frequency at which the active differential resistor 100Abehaves as a resistor may be set by the value of the blocking capacitorC1 106A.

The differential resistance of the diode is a function of the currentthat is running through it. Thus, the differential resistance of thediode can be programmed by the choice of current. Equation 2 belowprovides a diode expression that is useful to determine the current fora desired resistance value.

I(R)=1/(a*R)−Is  [EQ. 2]

Where:

-   -   I_(S) represents the saturation current of the diode.

The expression for term “a” is provided by Equation 3 below:

a=q/(n*k*T)  [EQ. 3]

Where:

-   -   q is the elementary charge (1.60217662e-19 coulombs);    -   k Boltzmann's constant (1.38064852 joules per kelvin);    -   n is the ideality factor (e.g., 1); and    -   T is the temperature (e.g., 300.15 kelvin).

Solving for “a,” one obtains 38.66. Accordingly, when using a diode witha saturation current (i.e., “Is”) of 1e⁻¹²A, to obtain a resistance of1KΩ across the diode D1 (108), the current I(R)=1/(a*R)−Is=25.86 uA.

The stochastic noise density, as provided by the voltage between thefirst node 102 and the second node 104, is governed by the shot noisecurrent through the diode instead of the Johnson-Nyquist noise of aconventional resistor.

The shot noise current through the diode D1 (108) is converted to avoltage by the impedance of the diode D1 (108). In the present example,this density may be 2.889 nV/Hz½, which is approximately 29% lower thanthe Johnson-Nyquist noise of a conventional resistor, which may have anoise density of 4.071 nV/Hz½. Thus, by virtue of using a combination ofa diode 108 in parallel with a current source 120 and a capacitor106A/106B coupled to a node of the active differential resistor100A/100B, the Johnson-Nyquist noise is essentially exchanged with shotnoise, which significantly lowers the overall noise of the resistanceelement.

With the foregoing example, it may now be helpful to provide amathematical explanation of the improvement in noise between using aconventional resistor and the active differential resistors 100A and100B disclosed herein. In this regard, the following expressions providethe theory behind the improvement identified by the present disclosureby way of mathematical derivation of the noise of the diode D1 (108).

The current versus voltage I(V) curve of an ideal diode may be given bythe expression of Equation 4 below:

I(V)=I _(S)*(e ^((a*v))−1)  [EQ. 4]

Where:

-   -   I(V) is the current through the diode D1 (108);    -   I_(S) represents the saturation current of the diode D1 (108);    -   V is the voltage across the diode D1 (108); and    -   a is provided by Equation 3 above.

The conduction of the diode may be expressed as an incremental change ofcurrent versus an incremental change of voltage, as provided in Equation5 below:

dI/dV=a*Is*e ^((a*V))  [EQ. 5]

The impedance, R, of the diode 108 may be expressed as an incrementalchange of voltage over an incremental change of time, as provided inEquation 6 below:

R=dV/dI=e ^((−a*v))/(a*Is)  [EQ. 6]

The above expression can be solved for diode voltage verses resistanceas provided by Equation 7 below:

V(R)=−log(a*Is*R)/a  [EQ. 7]

Equation 6 can be substituted in the original diode I(V) Equation 1above to provide the DC current to obtain a desired impedance R, asprovided by Equation 8 below:

I(R)=1/(a*R)−Is  [EQ. 8]

Upon determining the current that flows through the diode D1 (108) toobtain the desired resistance, the shot noise may also be determined.The RMS shot noise current per root Hz is given by Equation 9 below:

I _(SHOT) /√{square root over (Hz)}=√{square root over (2*q*I)}  [EQ. 9]

This shot noise current may be converted to voltage by that same diode'sdifferential impedance between the first node 102 and the second node104. Accordingly, the voltage noise per root Hertz across the diode D1(108) biased to an impedance R is provided by Equation 10 below:

V _(SHOT) /√{square root over (Hz)}=R*√{square root over(2*q*1/a*R-Is)}  [EQ. 10]

The ratio of shot noise to Johnson noise is provided by the expressionof Equation 11 below:

$\begin{matrix}{\frac{V_{SHOT}/\sqrt{Hz}}{V_{John}/\sqrt{Hz}} = \sqrt{\frac{n}{2} - {R*q*\frac{Is}{2*k*T}}}} & \left\lbrack {{EQ}.\mspace{14mu} 11} \right\rbrack\end{matrix}$

By way of demonstrative example, the expression of Equation 11 above canbe approximated to equal √{square root over (n/2)} since

$R*q*\frac{Is}{2*k*T}$

is small compared to √{square root over (n/2)}. Since the emissioncoefficient “n” is approximately equal to 1, the biased diode D1 (108)has approximately 29% (or 3 dB) less noise than a conventional passiveresistor. This result is independent of temperature. This result isindependent of temperature. Many would find this an unexpected resultsince shot noise is generally understood to be independent oftemperature while Johnson noise is generally understood to depend ontemperature as in Equation 1. However, a diode becomes more nonlinear asthe temperature decreases. Accordingly, the noise of the active resistordiscussed herein goes down with temperature (as does the Johnson-Nyquistnoise), since

$R*q*\frac{Is}{2*k*T}$

is small compared to √{square root over (n/2)}. Note that in the presentexample,

$R*q*\frac{Is}{2*k*T}$

is 1.9e-8 compared to 0.707 for √{square root over (n/2)}. However, inpractice a different bias current as given in Equation 8 is used at eachtemperature to achieve the same differential resistance due to thedependence of a and Is on temperature.

The foregoing derivation is for the case of an ideal scenario (e.g.,noiseless; current source and a diode with no terminal resistance). Butthe ideal performance indicated by the above theory is attainable with apractical circuit as confirmed by the applicant via an LTspicesimulation performed at 27° C., n=1, Is=1 pA, and a resistance value Rfor the active differential resistor 100A to be 1KΩ based on thepractical values depicted in FIG. 1A. In this regard it is noted thatthe LTspice simulator lends itself well for noise verification sinceJohnson-Nyquist and shot noises (e.g., their impact on circuit behavior)are computed from first principles. By way of practical example, thediode D1 (108) is assumed to be less than ideal in that it has 1Ω ofseries resistance. The current source 120 is implemented with a singleresistor R1 110 and a voltage source 112 providing 5V.

By way of comparison, for a conventional 1KΩ passive resistor, thecalculated Johnson-Nyquist noise is 4.0713715 nV/sqrt(Hz). The result ofthe LTspice simulation is 4.0713762 nV/sqrt(Hz), which confirms thecalculation. In contrast, the calculated shot noise for the activedifferential resistor 100A of FIG. 1A is calculated to be 2.8788944nV/sqrt(Hz). The result of the LTspice simulation is 2.8789013 nV, whichconfirms that calculation. Accordingly, the LTspice simulation confirmsthat a meaningful noise improvement can be obtained by using the activedifferential resistor 100A of FIG. 1A.

The applicant has discovered that some diode structures are moresuccessful in reducing the Johnson-Nyquist noise than others. Forexample, a PIN diode is a diode that has a wide, un-doped intrinsicsemiconductor region between a p-type semiconductor and an n-typesemiconductor region. Thus, in contrast to ordinary PN junction diodes,the wide intrinsic region makes the PIN diode not only an inferiorrectifier, but also does not provide substantial noise benefits. Indeed,since PIN diodes are more linear than a PN diode, they may not provide ameaningful noise benefit. Although there is a tradeoff betweenJohnson-Nyquist noise and shot noise, the shot noise introduced may berelatively high. That is because a PIN diode has a current versusvoltage I(V) curve indicating an ideality factor N=2, implying that ithas a large shot noise (e.g., which, in some scenarios, may be as largeas the Johnson-Nyquist noise). Accordingly, the applicant has discoveredthat by using a regular PN junction diode, the foregoing disadvantage ofa PIN diode is avoided.

Reference now is made to FIGS. 2A and 2B, which illustrate otherembodiments of active differential resistors 200A and 200B that use afield effect transistor (FET) as an active component to implement anactive differential resistor that may be used to replace a passiveresistor. Active differential resistors 200A and 200B have substantiallysimilar components except for different locations for a blockingcapacitor (i.e., 206A and 206B). Accordingly, aspects of the activedifferential resistors 200A and 200B will be discussed in the context of200A and will not be repeated for 200B for brevity. However, some of thedifferences will be highlighted.

Active differential resistor 200A includes a FET J1 (218), a firstvoltage source circuit 220, a second voltage source circuit 240, afeedback capacitor C2 (208), a blocking capacitor C3 (206A). In variousembodiments, the FET J1 (218) may be a junction field effect transistor(JFET) or a metal oxide semiconductor field effect transistor (MOSFET).

In various embodiments, the blocking capacitor C3 (206A/B) may becoupled between a first node 202 and the drain of the FET J1 (218), asillustrated in FIG. 2A, or between the source of the FET J1 (218) andthe second node 204 of the active differential resistor 200B, asillustrated in FIG. 2B.

The blocking capacitor C3 (206A/B) provides more flexibility (e.g.,broader application) to the active differential resistor 200A/B in thatit decouples the active differential resistor 200A/B from any circuitthat is coupled between its differential inputs 202 and 204. Putdifferently, by virtue of the decoupling capacitor C3 (206A/B) theactive differential resistor 200A/B can be used in different voltageenvironments. Thus, the drain 232 (or source 234) of the FET J1 (218)can be isolated from the actual voltage at the first node 202 or thesecond node 204. In one embodiment, the value of the blocking capacitorC3 (206A/B) is based on the lowest desired frequency of operation of thedifferential resistor 200A/B.

The active differential resistor 200A includes a first voltage sourcecircuit 220 coupled across (e.g., in parallel with) the drain 232 andsource 234 of the FET 218. Any suitable voltage source may be used toprovide the drain 232 to source 234 bias voltage of the FET J1 (218).For example, the first voltage source may include a direct currentvoltage source 212 coupled in series with a resistor R3 (216). Theactive differential resistor 200A includes a second voltage sourcecircuit 240 coupled between the gate and the source of the FET J1 (218).The second voltage source may include a direct current voltage source V2coupled in series with a resistor R2 (210). It is believed that thoseskilled in the art are familiar with other suitable voltage sourcecircuits, and they are therefore not discussed here in substantialdetail for brevity.

The first and the second voltage sources 220 and 240 operate together tobias the FET J1 (218) to be in or near the saturation region such thatthe channel current noise is due to shot noise instead ofJohnson-Nyquist noise. Put differently, the applicant has discoveredthat by virtue of biasing the FET J1 (232) to be in the saturationregion, the FET J1 (232) acts as an active differential resistor thattrades Johnson-Nyquist noise for shot noise, which provides an overalllower noise floor.

The larger the resistance of the resistor R3 (216), the lower the noiseintroduced by the resistor R3 (216) to the active differential resistor200A. In one embodiment, the value of the resistor R3 (216) of the firstvoltage source circuit 220, is chosen to be higher than the desiredimpedance of the active differential resistor 200A. For example, thehigher the value of the resistor R3 (216), the closer the activedifferential resistor 200A is in performance to the ideal performancelimit.

However, the value of resistor R3 (216) should be low enough such thatthe voltage provided by the first voltage source circuit 240 can supplyenough current into the drain of the FET J1 (218). Thus, the larger theresistance of resistor R3 (216), the larger the voltage drop across it,thereby reducing the voltage across the drain 232 to source 234 of theFET J1 (218). The resistance of resistor R3 (216) should be small enoughsuch that the voltage across FET J1 (218) is large enough to keep theFET in saturation region. In this regard, it is noted that thesaturation region of the FET J1 (218) is the where the drain 232 tosource 234 current, for a given gate to source 234 voltage (which issupplied by the second voltage source circuit 240), does notsubstantially increase with an increase in a drain 232 to source 234voltage (without reaching the breakdown region).

As to the resistance of the resistor R2 (210) of the second voltagesource circuit 240, in one embodiment, should also be chosen to behigher than the desired impedance of the active differential resistor200A. The value of the resistor R2 (210) may be set by the gate driverequirements of the FET J1 (218), which are typically very low involtage.

In one embodiment, there is a feedback capacitor C2 (208) coupledbetween the gate and drain 232 of the FET J1 (218) configured toproviding the appropriate impedance by reducing the impedance betweenthe drain 232 and gate via feedback. At higher frequencies, the gate ofthe FET J1 (218) is shorted to the drain 232. In one embodiment, thefeedback capacitor C2 (208) is coupled between the gate and the firstnode 202. The value of the feedback capacitor C2 (208) may be chosensuch that it provides a low impedance at the lowest frequency ofinterest compared to the desired impedance of the active differentialresistor 200A.

Similarly, in one embodiment, the value of the blocking capacitor C3(206A/B) can be based on providing a low impedance at the lowestfrequency at which the structure of FIG. 2A behaves as an activedifferential resistor. In this regard, it is noted that it may bedesirable to have a low noise RC circuit operated at frequencies thatare above and below the frequency set by the RC time constant of theblocking capacitor C3 (206A/B) and the resistance of the activedifferential resistor 200A/B.

FIGS. 2A and 2B illustrate, by way of example and not limitation, somecomponent values that may be used to implement a 1KΩ active differentialresistor at frequencies substantially above 159 Hz and as a capacitor atfrequencies substantially below 159 Hz. For example, at 159 Hz, theimpedance phase angle of the active differential resistor 200A or 200Bis approximately 45 degrees.

By way of demonstrative example, FIG. 2A illustrates the differentialimpedance between the first node 202 and the second node 204 to be 1KΩat frequencies of about 1 KHz. Significantly, the stochastic noisedensity across the first node 202 and the second node 204 is calculatedto be only 3.333 nV/Hz^(1/2), instead of 4.071 nV/Hz^(1/2) of aconventional passive 1KΩ resistor. Thus, in this example, theimprovement in noise is approximately 18% for a square law device, suchas the FET J1 (218).

Reference now is made to FIGS. 3A and 3B, which illustrate otherembodiments of active differential resistors 300A and 300B that use afield effect transistor (FET) and a transformer 340 to implement anactive differential resistor that may be used to replace a passiveresistor. Active differential resistors 300A and 300B provide a noiseimprovement over active differential resistors 200A and 200B and may bebest appreciated in contrast to FIGS. 2A and 2B.

Active differential resistors 300A and 300B have substantially similarcomponents to one-another, except for a different location of a blockingcapacitor (i.e., 306A and 306B). Accordingly, aspects of the activedifferential resistors 300A and 300B will be discussed in the context of300A and will not be repeated for 300B, for brevity. However, some ofthe differences will be highlighted.

Active differential resistor 300A includes a FET J2 (316), a transformer330, a first voltage source 312, a second voltage source 314, and ablocking capacitor C4 (306A). In various embodiments, the FET J2 (316)may be a JFET or a MOSFET.

In various embodiments, the blocking capacitor C4 (306A/B) may becoupled between a first node 202 and the drain 318 of the FET J2 (216),as illustrated in FIG. 3A, or between the source 320 of the FET J2 (216)and the second node 304 of the active differential resistor 300B, asillustrated in FIG. 3B.

The blocking capacitor C3 (306A/B) provides more flexibility (e.g.,broader application) to the active differential resistor 300A/B in thatit decouples the active differential resistor 300A/B from any circuitthat is coupled between its differential inputs 302 and 304. Putdifferently, by virtue of the decoupling capacitor C3 (306A or 306B) theactive differential resistor 300A/B can be used in different voltageenvironments. Thus, the drain 318 (or source 320) of the FET J2 (316)can be isolated from the actual voltage at the first node 302 or thesecond node 304. In one embodiment, the value of the blocking capacitorC4 (306A/B) is based on the lowest desired frequency of operation of thedifferential resistor 300A/B.

The transformer 340 includes a primary winding L1 (314) that has a firstend coupled to the gate and a second end coupled to the source of theFET J2 (316) via a first voltage source V4 (312). The secondary winding308 has a first end that is coupled to the drain and a second endcoupled to the source of the FET J2 (316) via a second voltage source V5(310). The transformer is configured to provide impedance to the drain318 of the FET J2 (316).

The active differential resistor 300A includes a first voltage source312 coupled between the second end of the primary winding L1 (314) andthe source of the FET J2 (316). There is a second voltage source V5(310) coupled between the second end of the secondary winding L2 (308)and the source of the FET J2 (316). Any suitable voltage source may beused to implement these voltage sources of FIGS. 3A and 3B. It isbelieved that those skilled in the art are familiar with other suitablevoltage source structures, and they are therefore not discussed here insubstantial detail, for brevity.

The first and the second voltage sources 312 and 310 operate together tobias the FET J2 (316) to be in or near the saturation region such thatthe channel current noise is due to shot noise instead ofJohnson-Nyquist noise. Accordingly, the applicant has discovered that byvirtue of biasing the FET J2 (316) to be in or near the saturationregion, the FET J2 (316) acts as an active differential resistor thattrades Johnson-Nyquist noise for shot noise, which provides a lowernoise floor. Further, by virtue of using a transformer 340, thenonlinearity of the FET J2 (316) is further exacerbated, therebyproviding more tradeoff between the Johnson-Nyquist noise and shotnoise. For example, for the same change in voltage provided by secondvoltage source V5 (310) to the drain 318 to source 320, there is alarger change in voltage from the gate to source 320.

FIGS. 3A and 3B illustrate, by way of example and not limitation, somecomponent values that may be used to implement a 1KΩ active differentialresistor at frequencies that are above 100 KHz. For example, aninductance ratio of L1 to L2 of 1:.01 (e.g., 1:100) ratio could be used,which provides a turn's ratio of (100)^(1/2)=1:10. Significantly, thenoise density above 100 kilohertz is only 1.058 nV/Hz^(1/2). Thus, theembodiment of FIG. 2A (or 2B) may provide 74% less noise than aconventional passive resistor. That is because the problematicJohnson-Nyquist noise is exchanged with the more manageable shot noise.In this regard, it is noted that the improvement in noise reduction mayincrease with the turns ratio of the transformer. The useable bandwidthof the low noise active differential resistor can be adjusted by thetransformer inductance and the blocking capacitor value 306A/B, usingwell known circuit analysis techniques such the complex impedance lawand nodal analysis.

Applications

The Johnson-Nyquist noise is generally regarded to be the fundamentalnoise limit of a device with an IV curve following Ohm's Law. By virtueof being unshackled by the above constraint based on the conceptsdiscussed herein, a differential resistor with less noise can be enjoyedby countless applications. For example, an active differential resistordiscussed herein may be used in the context of quiet termination intransmission line systems with low level signals, automatic testequipment of electronic amplifiers that allow input termination of a lownoise resistor to facilitate measuring the current noise of theamplifier without combining Johnson-Nyquist noise from the test fixture,physical sensors, etc.

For example, many physical sensors provide a current in response to asensed physical quantity. The signal amplitude may be proportional tothe termination impedance. However, such terminating impedance maysupply undesired noise to the signal. The active differential resistorsthat have been described herein may reduce the amount of noise suppliedby such termination.

FIG. 4 illustrates an example of an active differential resistor 402connected across an end of a transmission line 404 and configured tooperate as a low noise termination of that line.

FIG. 5 illustrates an example of an active differential resistor 502connected across an input of an electronic amplifier 504 and configuredto operate as part of an automated test equipment that determines thelevel of noise generated by the electronic amplifier.

FIG. 6 illustrates an example of an active differential resistor 602connected across an output of a physical sensor 604, such as acapacitance microphone. In various embodiments, the active differentialresistors illustrated in FIGS. 4 to 6 may be any of the type describedherein.

The benefits of the concepts discussed herein may be further appreciatedby way of comparative example. In a regular microphone system, asoundwave moves the diaphragm of the microphone, where the change indistance between the two charge bearing surfaces of the microphoneprovides a voltage. This voltage (representing the sound signal) may beof small amplitude (e.g., in the mV range). The larger the resistancethat is used at the output of the microphone sensor, the lower the noisein the system because the signal to noise ratio improves. However,Johnson noise is added at the square root of the resistance. Thus, thesignal to noise ratio improves with the square root of the resistancevalue. Put differently, a larger resistance is typically preferred.However, a large resistance may lead to a larger time constant becauseof the capacitive element of the microphone, thereby reducing thebandwidth. Thus, while in traditional microphone systems larger valueresistors may be preferred to reduce the noise in a microphone system,it comes at the cost of reduced bandwidth.

However, using the concepts discussed herein, a lower resistance valuecould be used, thereby dramatically improving the bandwidth of themicrophone, while maintaining or even lowering the signal to noise ratioof the microphone system.

CONCLUSION

The components, steps, features, objects, benefits, and advantages thathave been discussed are merely illustrative. None of them, nor thediscussions relating to them, are intended to limit the scope ofprotection in any way. Numerous other embodiments are also contemplated.These include embodiments that have fewer, additional, and/or differentcomponents, steps, features, objects, benefits, and/or advantages. Thesealso include embodiments in which the components and/or steps arearranged and/or ordered differently.

For example, the diodes of FIGS. 1A and 1B can be any PN junction, suchas the base-emitter junction of a bipolar transistor, the PN junction ofa JFET, the PN junction between the drain/source and substrate of aMOSFET, etc. Additionally, the biasing of any embodiment shown can beelectronically controlled to make the resistance of the activedifferential resistor electronically controlled.

Unless otherwise stated, all measurements, values, ratings, positions,magnitudes, sizes, and other specifications that are set forth in thisspecification, are approximate, not exact. They are intended to have areasonable range that is consistent with the functions to which theyrelate and with what is customary in the art to which they pertain.

Except as stated immediately above, nothing that has been stated orillustrated is intended or should be interpreted to cause a dedicationof any component, step, feature, object, benefit, advantage, orequivalent to the public, regardless of whether it is or is not recitedin the claims.

All articles, patents, patent applications, and other publications thathave been cited in this disclosure are incorporated herein by reference.

It will be understood that the terms and expressions used herein havethe ordinary meaning as is accorded to such terms and expressions withrespect to their corresponding respective areas of inquiry and studyexcept where specific meanings have otherwise been set forth herein.Relational terms such as “first” and “second” and the like may be usedsolely to distinguish one entity or action from another, withoutnecessarily requiring or implying any actual relationship or orderbetween them. The terms “comprises,” “comprising,” and any othervariation thereof when used in connection with a list of elements in thespecification or claims are intended to indicate that the list is notexclusive and that other elements may be included. Similarly, an elementpreceded by an “a” or an “an” does not, without further constraints,preclude the existence of additional elements of the identical type.

The Abstract of the Disclosure is provided to allow the reader toquickly ascertain the nature of the technical disclosure. It issubmitted with the understanding that it will not be used to interpretor limit the scope or meaning of the claims. In addition, in theforegoing Detailed Description, it can be seen that various features aregrouped together in various embodiments for the purpose of streamliningthe disclosure. This method of disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter lies in less than allfeatures of a single disclosed embodiment. Thus the following claims arehereby incorporated into the Detailed Description, with each claimstanding on its own as a separately claimed subject matter.

What is claimed is:
 1. An active differential resistor, comprising: aninput node and an output node operative to provide a differentialresistance; a diode having a first node and a second node; a capacitorcoupled in series between the first node of the diode and the inputnode; a current source coupled across the first node and the second nodeof the diode and configured to forward bias the diode such that aJohnson-Nyquist noise of the active differential resistor is replaced bya shot noise.
 2. The active differential resistor of claim 1, whereinthe first node of the diode is a cathode and the second node of thediode is an anode.
 3. The active differential resistor of claim 1,wherein the first node of the diode is an anode and the second node ofthe diode is a cathode.
 4. The active differential resistor of claim 1,wherein current source comprises a voltage source in series with aresistor.
 5. The active differential resistor of claim 1, wherein thecapacitor is configured to decouple the active differential resistorfrom a circuit coupled between the input node and the output node, suchthat the active differential resistor can operate in a voltageenvironment that is independent of the circuit coupled thereto.
 6. Theactive differential resistor of claim 1, wherein a capacitance of thecapacitor is based on a lowest desired frequency of operation of theactive differential resistor for a predetermined resistance between theinput node and the output node.
 7. The active differential resistor ofclaim 1, wherein: the diode comprises a junction gate field-effecttransistor (JFET), and a drain and a source of the JFET are connectedtogether.
 8. An active differential resistor, comprising: an input nodeand an output node; a field effect transistor (FET) having a draincoupled to the input node and a source coupled to the output node; afirst voltage source circuit coupled between the drain and the source ofthe FET; and a second voltage source circuit coupled between a gate andthe source of the FET, wherein the first and second voltage sourcecircuits are configured to bias the FET into a saturation region, suchthat a Johnson-Nyquist noise of the active differential resistor isreplaced by a shot noise.
 9. The active differential resistor of claim8, further comprising a decoupling capacitor coupled between the inputnode and the drain of the FET, wherein the decoupling capacitor isconfigured to decouple the active differential resistor from a circuitcoupled between the input node and the output node, such that the activedifferential resistor can operate in a voltage environment that isindependent from the circuit coupled thereto.
 10. The activedifferential resistor of claim 8, further comprising a decouplingcapacitor coupled between the output node and the source of the FET,wherein the decoupling capacitor is configured to decouple the activedifferential resistor from a circuit coupled between the input node andthe output node, such that the active differential resistor can operatein a voltage environment that is independent from the circuit coupledthereto.
 11. The active differential resistor of claim 8, wherein acapacitance of the decoupling capacitor is based on a lowest frequencyof operation of the active differential resistor for a predeterminedresistance between the input node and the output node.
 12. The activedifferential resistor of claim 8, further comprising a feedbackcapacitor coupled between the drain and the gate of the FET, wherein thefeedback capacitor is configured to reduce an impedance between thedrain and the gate via feedback.
 13. The active differential resistor ofclaim 8, further comprising a feedback capacitor coupled between theinput and the gate of the FET, wherein the feedback capacitor isconfigured to reduce an impedance between the drain and the gate viafeedback.
 14. The active differential resistor of claim 8, wherein thefirst and second voltage source circuits each comprise a direct current(DC) voltage source in series with a resistor.
 15. The activedifferential resistor of claim 14, wherein the resistor of the firstvoltage source circuit has a resistance that is larger than an impedancebetween the input node and the output node of the active differentialresistor.
 16. The active differential resistor of claim 15, wherein theresistor of the second voltage source circuit has a resistance that islarger than an impedance between the input node and the output node ofthe active differential resistor.
 17. The active differential resistorof claim 8, wherein the first and second voltage source circuits operatetogether to forward bias the FET into or near a saturation region. 18.The active differential resistor of claim 8, wherein the FET is ajunction field effect transistor (JFET).
 19. An active differentialresistor, comprising: an input node and an output node; a field effecttransistor (FET) having a drain coupled to the input node and a sourcecoupled to the output node; a transformer having a primary winding and asecondary winding, wherein a first end of the primary winding isconnected to a gate of the FET and a first end of the secondary windingis connected to a drain of the FET; a first voltage source coupledbetween a second end of the primary winding and a source of the FET andconfigured to bias the gate of the FET; and a second voltage sourcecircuit coupled between a second end of the secondary winding and thesource of the FET and configured to bias the drain of the FET, whereinthe first and second voltage source circuits are configured to bias theFET into or near a saturation region such that a Johnson-Nyquist noiseof the active differential resistor is replaced by a shot noise.
 20. Theactive differential resistor of claim 19, wherein the transformer isconfigured to enhance a nonlinearity of the FET in that a change involtage provided by the second voltage source across the drain to thesource results in a larger change in voltage across the gate to thesource of the FET.
 21. The active differential resistor of claim 19,wherein the transformer has an inductance ratio of at least 1:100between the primary winding and the secondary winding.
 22. The activedifferential resistor of claim 19, wherein the active differentialresistor is configured to have less noise the larger a turn ratio isbetween the primary winding and the secondary winding.
 23. The activedifferential resistor of claim 19, further comprising a decouplingcapacitor coupled between the input and the drain of the FET, whereinthe decoupling capacitor is configured to decouple the activedifferential resistor from a circuit coupled between the input node andthe output node, such that the active differential resistor can operatein a voltage environment that is independent from the circuit coupledthereto.
 24. The active differential resistor of claim 19, furthercomprising a decoupling capacitor coupled between the output node andthe source of the FET, wherein the decoupling capacitor is configured todecouple the active differential resistor from a circuit coupled betweenthe input node and the output node, such that the active differentialresistor can operate in a voltage environment that is independent fromthe circuit coupled thereto.
 25. The active differential resistor ofclaim 19, wherein a capacitance of the decoupling capacitor is based ona lowest frequency of operation of the active differential resistor fora predetermined resistance between the input node and the output node.26. The active differential resistor of claim 19, wherein the FET is ajunction field effect transistor (JFET).
 27. A transmission lineterminated by the active differential resistor of claim
 19. 28. Aphysical sensor comprising the active differential resistor of claim 19coupled to an output of the physical sensor.
 29. An electronic amplifiercomprising the active differential resistor of claim 19 coupled to aninput of the electronic amplifier.
 30. A method of providing adifferential resistance using a FET, comprising: applying a firstvoltage level to a gate of the FET; applying a second voltage level to adrain of the FET; placing the FET into a saturation region via the firstvoltage level and the second voltage level; and replacing aJohnson-Nyquist noise of the active differential resistor by a shotnoise such that an overall noise-floor of the differential resistance isreduced.
 31. The active differential resistor of claim 30, furthercomprising decoupling the active differential resistor from a circuitconnected to the active differential resistor, such that the activedifferential resistor can operate in a voltage environment that isindependent from the circuit connected thereto.
 32. The activedifferential resistor of claim 30, further comprising varying a secondvoltage level at the gate of the FET based on a gain factor with respectto a second voltage level at the drain of the FET.
 33. The activedifferential resistor of claim 31, further comprising inductivelycoupling the second voltage at the drain of the FET to the gate of theFET via a transformer, wherein the gain factor is provided by a turnratio of the transformer.